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Cao Z, Bao R, Hou Z. Cascade-enhanced transport efficiency of biochemical systems. CHAOS (WOODBURY, N.Y.) 2023; 33:2894486. [PMID: 37276569 DOI: 10.1063/5.0146769] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/16/2023] [Accepted: 05/08/2023] [Indexed: 06/07/2023]
Abstract
Recent developments in nonequilibrium thermodynamics, known as thermodynamic uncertainty relations, limit the system's accuracy by the amount of free-energy consumption. A transport efficiency, which can be used to characterize the capacity to control the fluctuation by means of energy cost, is a direct result of the thermodynamic uncertainty relation. According to our previous research, biochemical systems consume much lower energy cost by noise-induced oscillations to keep almost equal efficiency to maintain precise processes than that by normal oscillations. Here, we demonstrate that the performance of noise-induced oscillations propagating can be further improved through a cascade reaction mechanism. It has been discovered that it is possible to considerably enhance the transport efficiency of the biochemical reactions attained at the terminal cell, allowing the cell to use the cascade reaction mechanism to operate more precisely and efficiently. Moreover, an optimal reaction coupling strength has been predicted to maximize the transport efficiency of the terminal cell, uncovering a concrete design strategy for biochemical systems. By using the local mean field approximation, we have presented an analytical framework by extending the stochastic normal form equation to the system perturbed by external signals, providing an explanation of the optimal coupling strength.
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Affiliation(s)
- Zhiyu Cao
- Department of Chemical Physics and Hefei National Laboratory for Physical Sciences at Microscales, iChEM, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Ruicheng Bao
- Department of Chemical Physics and Hefei National Laboratory for Physical Sciences at Microscales, iChEM, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Zhonghuai Hou
- Department of Chemical Physics and Hefei National Laboratory for Physical Sciences at Microscales, iChEM, University of Science and Technology of China, Hefei, Anhui 230026, China
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2
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Cao Z, Hou Z. Improved estimation for energy dissipation in biochemical oscillations. J Chem Phys 2022; 157:025102. [DOI: 10.1063/5.0092126] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Biochemical oscillations, regulating the timing of life processes, need consume energy to achieve good performance on crucial functions, such as high accuracy of phase period and high sensitivity to external signals. However, it is a great challenge to precisely estimate the energy dissipation in such systems. Here, based on the stochastic normal form theory (SNFT), we calculate the Pearson correlation coefficient between the oscillatory amplitude and phase, and a trade-off relation between transport efficiency and phase sensitivity can then be derived, which serves as a tighter form than the estimator resulting from the conventional thermodynamic uncertainty relation (TUR). Our findings demonstrate that a more precise energy dissipation estimation can be obtained by enhancing the sensitivity of the biochemical oscillations. Moreover, the internal noise and amplitude power effects have also been discovered.
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Affiliation(s)
- Zhiyu Cao
- Department of Chemical Physics and Hefei National Laboratory for Physical Sciences at Microscales, iChEM, University of Science and Technology of China, University of Science and Technology of China Department of Chemical Physics, China
| | - Zhonghuai Hou
- Department of Chemical Physics, University of Science and Technology of China Hefei National Laboratory for Physical Sciences at the Microscale, China
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3
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Nguyen B, Seifert U, Barato AC. Phase transition in thermodynamically consistent biochemical oscillators. J Chem Phys 2018; 149:045101. [PMID: 30068193 DOI: 10.1063/1.5032104] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022] Open
Abstract
Biochemical oscillations are ubiquitous in living organisms. In an autonomous system, not influenced by an external signal, they can only occur out of equilibrium. We show that they emerge through a generic nonequilibrium phase transition, with a characteristic qualitative behavior at criticality. The control parameter is the thermodynamic force which must be above a certain threshold for the onset of biochemical oscillations. This critical behavior is characterized by the thermodynamic flux associated with the thermodynamic force, its diffusion coefficient, and the stationary distribution of the oscillating chemical species. We discuss metrics for the precision of biochemical oscillations by comparing two observables, the Fano factor associated with the thermodynamic flux and the number of coherent oscillations. Since the Fano factor can be small even when there are no biochemical oscillations, we argue that the number of coherent oscillations is more appropriate to quantify the precision of biochemical oscillations. Our results are obtained with three thermodynamically consistent versions of known models: the Brusselator, the activator-inhibitor model, and a model for KaiC oscillations.
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Affiliation(s)
- Basile Nguyen
- II. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart, Germany
| | - Udo Seifert
- II. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart, Germany
| | - Andre C Barato
- Max Planck Institute for the Physics of Complex Systems, Nöthnizer Strasse 38, 01187 Dresden, Germany
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Mahara H, Yamaguchi T, Parmananda P. Stochastic resonance with a mesoscopic reaction-diffusion system. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:062913. [PMID: 25019857 DOI: 10.1103/physreve.89.062913] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/12/2013] [Indexed: 06/03/2023]
Abstract
In a mesoscopic reaction-diffusion system with an Oregonator reaction model, we show that intrinsic noise can drive a resonant stable pattern in the presence of the initial subthreshold perturbations. Both spatially periodic and aperiodic stochastic resonances are demonstrated by employing the Gillespies stochastic simulation algorithm. The mechanisms for these phenomena are discussed.
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Affiliation(s)
- Hitoshi Mahara
- Department of Physics, India Institute of Technology Bombay, Powai, Mumbai 400076, India and AIST, Higashi 1-1-1, Central 5-2, Tsukuba, Ibaraki, Japan
| | | | - P Parmananda
- Department of Physics, India Institute of Technology Bombay, Powai, Mumbai 400076, India
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Cantini L, Cianci C, Fanelli D, Massi E, Barletti L. Linear noise approximation for stochastic oscillations of intracellular calcium. J Theor Biol 2014; 349:92-9. [PMID: 24503287 DOI: 10.1016/j.jtbi.2014.01.035] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/11/2013] [Revised: 01/07/2014] [Accepted: 01/24/2014] [Indexed: 12/22/2022]
Abstract
A stochastic model of intracellular calcium oscillations is analytically studied. The governing master equation is expanded under the linear noise approximation and a closed prediction for the power spectrum of fluctuations analytically derived. A peak in the obtained power spectrum profile signals the presence of stochastic, noise induced oscillations which extend also outside the region where a deterministic limit cycle is predicted to occur.
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Affiliation(s)
- Laura Cantini
- Dipartimento di Matematica e Informatica "U. Dini", University of Florence, Viale Morgagni 67/A, 50139 Florence, Italy
| | - Claudia Cianci
- Dipartimento di Sistemi e Informatica and INFN, University of Florence, Via S. Marta 3, 50139 Florence, Italy
| | - Duccio Fanelli
- Dipartimento di Fisica e Astronomia, University of Florence and INFN, Via Sansone 1, 50019 Sesto Fiorentino, Florence, Italy
| | - Emma Massi
- Dipartimento di Matematica e Informatica "U. Dini", University of Florence, Viale Morgagni 67/A, 50139 Florence, Italy
| | - Luigi Barletti
- Dipartimento di Matematica e Informatica "U. Dini", University of Florence, Viale Morgagni 67/A, 50139 Florence, Italy
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6
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Rao T, Xiao T, Hou Z. Entropy production in a mesoscopic chemical reaction system with oscillatory and excitable dynamics. J Chem Phys 2012; 134:214112. [PMID: 21663349 DOI: 10.1063/1.3598111] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
Stochastic thermodynamics of chemical reaction systems has recently gained much attention. In the present paper, we consider such an issue for a system with both oscillatory and excitable dynamics, using catalytic oxidation of carbon monoxide on the surface of platinum crystal as an example. Starting from the chemical Langevin equations, we are able to calculate the stochastic entropy production P along a random trajectory in the concentration state space. Particular attention is paid to the dependence of the time-averaged entropy production P on the system size N in a parameter region close to the deterministic Hopf bifurcation (HB). In the large system size (weak noise) limit, we find that P ∼ N(β) with β = 0 or 1, when the system is below or above the HB, respectively. In the small system size (strong noise) limit, P always increases linearly with N regardless of the bifurcation parameter. More interestingly, P could even reach a maximum for some intermediate system size in a parameter region where the corresponding deterministic system shows steady state or small amplitude oscillation. The maximum value of P decreases as the system parameter approaches the so-called CANARD point where the maximum disappears. This phenomenon could be qualitatively understood by partitioning the total entropy production into the contributions of spikes and of small amplitude oscillations.
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Affiliation(s)
- Ting Rao
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Chemical Physics, University of Science and Technology of China, Hefei, Anhui, 230026, People's Republic of China
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Hao Y, Gong Y, Lin X, Wang L. Multiple resonances with time delays in scale-free networks of Hodgkin-Huxley neurons subjected to non-Gaussian noise. Sci China Chem 2011. [DOI: 10.1007/s11426-011-4268-0] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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8
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Zhang R, Xiao T, Hou Z. Internal noise enhanced oscillation in a delayed circadian pacemaker. Biophys Chem 2011; 158:54-60. [PMID: 21605935 DOI: 10.1016/j.bpc.2011.05.003] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/18/2011] [Revised: 04/28/2011] [Accepted: 05/01/2011] [Indexed: 10/18/2022]
Abstract
The effect of internal noise in a delayed circadian oscillator is studied by using both chemical Langevin equations and stochastic normal form theory. It is found that internal noise can induce circadian oscillation even if the delay time τ is below the deterministic Hopf bifurcation τ(h). We use signal-to-noise ratio (SNR) to quantitatively characterize the performance of such noise induced oscillations and a threshold value of SNR is introduced to define the so-called effective oscillation. Interestingly, the τ-range for effective stochastic oscillation, denoted as Δτ(EO), shows a bell-shaped dependence on the intensity of internal noise which is inversely proportional to the system size. We have also investigated how the rates of synthesis and degradation of the clock protein influence the SNR and thus Δτ(EO). The decay rate K(d) could significantly affect Δτ(EO), while varying the gene expression rate K(e) has no obvious effect if K(e) is not too small. Stochastic normal form analysis and numerical simulations are in good consistency with each other. This work provides us comprehensive understandings of how internal noise and time delay work cooperatively to influence the dynamics of circadian oscillations.
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Affiliation(s)
- Ruiting Zhang
- Hefei National Laboratory for Physical Sciences at Microscales, University of Science and Technology of China, Anhui, China
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9
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Non-Gaussian noise-optimized intracellular cytosolic calcium oscillations. Biosystems 2011; 103:13-7. [DOI: 10.1016/j.biosystems.2010.09.006] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/12/2010] [Revised: 08/25/2010] [Accepted: 09/08/2010] [Indexed: 11/22/2022]
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Bishop LM, Qian H. Stochastic bistability and bifurcation in a mesoscopic signaling system with autocatalytic kinase. Biophys J 2010; 98:1-11. [PMID: 20074511 DOI: 10.1016/j.bpj.2009.09.055] [Citation(s) in RCA: 74] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/17/2009] [Revised: 09/11/2009] [Accepted: 09/14/2009] [Indexed: 11/28/2022] Open
Abstract
Bistability is a nonlinear phenomenon widely observed in nature including in biochemical reaction networks. Deterministic chemical kinetics studied in the past has shown that bistability occurs in systems with strong (cubic) nonlinearity. For certain mesoscopic, weakly nonlinear (quadratic) biochemical reaction systems in a small volume, however, stochasticity can induce bistability and bifurcation that have no macroscopic counterpart. We report the simplest yet known reactions involving driven phosphorylation-dephosphorylation cycle kinetics with autocatalytic kinase. We show that the noise-induced phenomenon is correlated with free energy dissipation and thus conforms with the open-chemical system theory. A previous reported noise-induced bistability in futile cycles is found to have originated from the kinase synchronization in a bistable system with slow transitions, as reported here.
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Affiliation(s)
- Lisa M Bishop
- Department of Applied Mathematics, University of Washington, Seattle, Washington, USA.
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Ma J, Xiao T, Hou Z, Xin H. Coherence resonance induced by colored noise near Hopf bifurcation. CHAOS (WOODBURY, N.Y.) 2008; 18:043116. [PMID: 19123626 DOI: 10.1063/1.3013178] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/27/2023]
Abstract
Effects of colored noise near supercritical Hopf bifurcation, especially noise induced oscillation (NIO) and coherence resonance (CR), have been studied analytically in the Brusselator model, using the stochastic normal form method. Two types of colored noise are considered: one is the standard Gaussian colored noise generated by the Ornstein-Uhlenbeck (OU) process and the other is the so-called power-limited (PL) process. Depending on the noise intensity and noise type, it is found that the autocorrelation time, most probable radius and signal to noise ratio of the NIO may show nontrivial dependencies on the noise correlation time tau(c). Interestingly, for OU-type noise with intensity above a threshold, SNR is a bell-shaped function of tau(c), indicating enhancement of CR by noise correlation; and for PL-type noise, SNR may show double maxima when tau(c) is changed, demonstrating a new kind of multiresonance phenomenon. These theoretical predictions are well reproduced by numerical simulations.
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Affiliation(s)
- Juan Ma
- Department of Chemical Physics, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China
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Xiao TJ, Hou Z, Xin H. Entropy production and fluctuation theorem along a stochastic limit cycle. J Chem Phys 2008; 129:114506. [DOI: 10.1063/1.2978179] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Ma J, Hou ZH, Xin HW. Coherent Resonance for Rate Oscillations During CO Oxidation on Pt(110) Surfaces: Interplay Between Internal and External Noise. CHINESE J CHEM PHYS 2008. [DOI: 10.1088/1674-0068/21/04/339-345] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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15
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Abstract
Circadian rhythmic processes, mainly regulated by gene expression at the molecular level, have inherent stochasticity. Their robustness or resistance to internal noise has been extensively investigated by most of the previous studies. This work focuses on the constructive roles of internal noise in a reduced Drosophila model, which incorporates negative and positive feedback loops, each with a time delay. It is shown that internal noise sustains reliable oscillations with periods close to 24 h in a region of parameter space, where the deterministic kinetics would evolve to a stable steady state. The amplitudes of noise-sustained oscillations are significantly affected by the variation of internal noise level, and the best performance of the oscillations could be found at an optimal noise intensity, indicating the occurrence of intrinsic coherence resonance. In the oscillatory region of the deterministic model, the coherence of noisy circadian oscillations is suppressed by internal noise, while the period remains nearly constant over a large range of noise intensity, demonstrating robustness of the Drosophila model for circadian rhythms to intrinsic noise. In addition, the effects of time delay in the positive feedback on the oscillations are also investigated. It is found that the time delay could efficiently tune the performance of the noise-sustained oscillations. These results might aid understanding of the exploitation of intracellular noise in biochemical and genetic regulatory systems.
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Juan M, Hou Z, Xin H. Theoretical Study on the Effects of Internal Noise for Rate Oscillations during CO Oxidation on Platinum(110) Surfaces. J Phys Chem A 2007; 111:11500-5. [DOI: 10.1021/jp073890e] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Ma Juan
- Department of Chemical Physics, Hefei National Lab of Physical Science at Microscale, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China
| | - Zhonghuai Hou
- Department of Chemical Physics, Hefei National Lab of Physical Science at Microscale, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China
| | - Houwen Xin
- Department of Chemical Physics, Hefei National Lab of Physical Science at Microscale, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China
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